Gas turbine engine airfoil frequency design

ABSTRACT

A turbomachine airfoil element includes an airfoil that has pressure and suction sides spaced apart from one another in a thickness direction and joined to one another at leading and trailing edges. The airfoil extends in a radial direction a span that is in a range of 0.75-0.85 inch (19.1-21.6 mm). A chord length extends in a chordwise direction from the leading edge to the trailing edge at 50% span and is in a range of 0.56-0.66 inch (14.2-16.8 mm). The airfoil element includes at least two of a first mode with a frequency of 2740±10% Hz, a second mode with a frequency of 5956±10% Hz, a third mode with a frequency of 6554±10% Hz and a fourth mode with a frequency of 31959±10% Hz.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claim priority to U.S. Provisional Application No.62/446,920, filed on Jan. 17, 2017.

BACKGROUND

The disclosure relates to turbomachinery. More particularly, thedisclosure relates to gas turbine engine airfoils and their designedvibrational responses.

Airfoils of turbine engine blades and vanes are subject to a number ofperformance-affecting conditions. The airfoils are subject toenvironmental exposure and thermal and mechanical loading. These factorsare significant in each section of the engine for a variety of reasons.For example, in the fan section of high bypass engines, the airfoilshave a large diameter with a relatively small thickness. In a highpressure compressor and in a turbine section, the airfoil is exposed tohigh temperatures. Cooling passages are provided in the turbine sectionairfoils, but such cooling passages are typically absent in thecompressor section. For blades, rotational forces are also a significantdynamic stimulus.

Vibrational responses of the airfoil can provide an indication of howdurable the airfoil will be during engine operation. If an airfoiloperates too long at a resonant frequency during engine operation, thelife of the airfoil may be significantly shortened as the airfoil ismore highly stressed. An exemplary vibrational testing method is definedin United States Federal Aviation Administration (FAA) Advisory Circular38.83-1 (Sep. 8, 2009). Designing airfoils with desirable resonantfrequencies can prolong the useful life of engine components,particularly the airfoil itself.

SUMMARY

In one exemplary embodiment, a turbomachine airfoil element includes anairfoil that has pressure and suction sides spaced apart from oneanother in a thickness direction and joined to one another at leadingand trailing edges. The airfoil extends in a radial direction a spanthat is in a range of 0.75-0.85 inch (19.1-21.6 mm). A chord lengthextends in a chordwise direction from the leading edge to the trailingedge at 50% span and is in a range of 0.56-0.66 inch (14.2-16.8 mm). Theairfoil element includes at least two of a first mode with a frequencyof 2740±10% Hz, a second mode with a frequency of 5956±10% Hz, a thirdmode with a frequency of 6554±10% Hz and a fourth mode with a frequencyof 31959±10% Hz.

In a further embodiment of the above, three of the first, second, thirdand fourth mode frequencies are present.

In a further embodiment of any of the above, the first mode is a 1EBmode. The second mode is a 1TEB-SH mode. The third mode is a 1T mode andthe fourth mode is a 1CWB-SH mode.

In a further embodiment of any of the above, the 1EB and 1TEB-SH modescorrespond to deflections substantially parallel to thickness direction.The 1CWB-SH modes correspond to bending that is substantially normal tothe thickness direction and substantially along the chordwise direction.The 1T mode corresponds to twisting about the radial direction.

In a further embodiment of any of the above, the frequencies are at zerospeed and ambient conditions.

In a further embodiment of any of the above, at a runningspeed/condition the first mode has a frequency of 2593±10% Hz, thesecond mode has a frequency of 5638±10% Hz, the third mode has afrequency of 6205±10% Hz and the fourth mode has a frequency of30254±10% Hz.

In a further embodiment of any of the above, the frequencies are ±5% Hz.

In a further embodiment of any of the above, the airfoil element is acantilevered stator vane.

In a further embodiment of any of the above, the airfoil is anickel-based superalloy.

In a further embodiment of any of the above, the nickel-based superalloyhas a density of about 0.28-0.32 lb/in³ (7.7-8.9 g/cm³).

In a further embodiment of any of the above, the nickel-based superalloyhas a modulus of elasticity of about 27-36 Mpsi (186-248 GPa) at roomtemperature.

In another exemplary embodiment, a method of repairing an airfoilincludes the steps of providing an airfoil having pressure and suctionsides spaced apart from one another in a thickness direction and joinedto one another at leading and trailing edges. The airfoil extends in aradial direction a span that is in a range of 0.75-0.85 inch (19.1-21.6mm). A chord length extends in a chordwise direction from the leadingedge to the trailing edge at 50% span is in a range of 0.56-0.66 inch(14.2-16.8 mm). The provided airfoil has at least one unrestored modefrequency that is attributable to damage to the airfoil. The airfoil isrepaired to provide at least two of a first mode has a frequency of2740±10% Hz, a second mode has a frequency of 5956±10% Hz, a third modehas a frequency of 6554±10% Hz and a fourth mode has a frequency of31959±10% Hz. At least one of the first, second, third and fourth modefrequencies corresponds to a restored mode frequency that supersedes theunrestored mode frequency.

In a further embodiment of any of the above, the first mode is a 1EBmode, the second mode is a 1TEB-SH mode, the third mode is a 1T mode,and the fourth mode is a 1CWB-SH mode. The frequencies are at zero speedand ambient conditions. The airfoil is a nickel-based superalloy.

In another exemplary embodiment, a turbofan engine includes a fansection and a compressor section arranged fluidly downstream from thefan section. A turbine section is arranged fluidly downstream from thecompressor section. A combustor is arranged fluidly between thecompressor and turbine sections. An airfoil is in at least one of thefan, compressor and turbine sections. The airfoil has pressure andsuction sides spaced apart from one another in a thickness direction andjoined to one another at leading and trailing edges. The airfoil extendsin a radial direction a span that is in a range of 0.75-0.85 inch(19.1-21.6 mm). A chord length extends in a chordwise direction from theleading edge to the trailing edge at 50% span and is in a range of0.56-0.66 inch (14.2-16.8 mm). At least two of a first mode has afrequency of 2740±10% Hz, a second mode has a frequency of 5956±10% Hz,a third mode has a frequency of 6554±10% Hz and a fourth mode has afrequency of 31959±10% Hz.

In a further embodiment of any of the above, the airfoil is provided inthe compressor section.

In a further embodiment of any of the above, the compressor sectionincludes a high pressure compressor fluidly downstream from a lowpressure compressor. The airfoil is in the high pressure compressor.

In a further embodiment of any of the above, the airfoil element is partof a stator. The stator is a cantilevered stator vane.

In a further embodiment of any of the above, the high pressurecompressor includes eight stages.

In a further embodiment of any of the above, the airfoil is anickel-based superalloy with a density of about 0.28-0.32 lb/in³(7.7-8.9 g/cm³) and with a modulus of elasticity of about 27-36 Mpsi(186-248 GPa) at room temperature.

In a further embodiment of any of the above, the first mode is a 1EBmode. The second mode is a 1TEB-SH mode. The third mode is a 1T mode andthe fourth mode is a 1CWB-SH mode. The 1EB and 1TEB-SH modes correspondto deflections substantially parallel to thickness direction. The1CWB-SH modes correspond to bending that is substantially normal to thethickness direction and substantially along the chordwise direction. The1T mode corresponds to twisting about the radial direction.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be further understood by reference to the followingdetailed description when considered in connection with the accompanyingdrawings wherein:

FIG. 1A is a view of a perspective view of an example airfoil element.

FIG. 1B is top view of the airfoil of FIG. 1A.

FIG. 2 is a schematic sectional view of a fan section, a low pressurecompressor and a high pressure compressor of an example turbofan engine.

FIG. 3 is a schematic perspective view of an example fan blade and aportion of a fan hub.

FIG. 4A is a schematic perspective view of an integrally bladed rotor.

FIG. 4B is a schematic perspective view of a compressor blade airfoilwith a root.

FIG. 5A is a schematic side view of a cantilevered stator vane.

FIG. 5B is a schematic side view of a stator vane with an inner diametershroud.

FIG. 5C is a schematic side view of an adjustable inlet guide vane.

FIG. 6A is a schematic side view of an airfoil showing a first easywisebending mode node line.

FIG. 6B is an inward view of the airfoil of FIG. 6A with one vibrationalextreme shown in broken lines.

FIG. 6C is a front view of the airfoil of FIG. 6A with both vibrationalextremes shown in broken lines.

FIG. 6D is a front view of an airfoil with second easywise bending modeextremes shown in broken lines.

FIG. 6E is a front view of an airfoil with third easywise bending modeextremes shown in broken lines.

FIG. 7A is a side view of an airfoil showing a torsion mode node line.

FIG. 7B is an inward view of the airfoil of FIG. 7A, with one torsionalextreme shown in broken lines.

FIG. 8A is a side view of an airfoil showing a first stiffwise bendingmode node line.

FIG. 8B is an inward view of the airfoil of FIG. 8A with a rearwardvibrational extreme shown in broken lines.

FIG. 9A is a front view of a circumferential array of stator vanes.

FIG. 9B is a side view of the array of FIG. 9A with an axial vibrationalextreme shown in broken lines.

FIG. 10 is a Campbell diagram of an airfoil.

FIG. 11 is a schematic sectional view of a turbofan engine.

The embodiments, examples and alternatives of the preceding paragraphs,the claims, or the following description and drawings, including any oftheir various aspects or respective individual features, may be takenindependently or in any combination. Features described in connectionwith one embodiment are applicable to all embodiments, unless suchfeatures are incompatible. Like reference numbers and designations inthe various drawings indicate like elements.

DETAILED DESCRIPTION

FIG. 11 schematically illustrates a gas turbine engine 320. Theexemplary gas turbine engine 320 is a two-spool turbofan engine thatgenerally incorporates a fan section 322, a compressor section 324, acombustor section 326 and a turbine section 328. Alternative enginesmight include an augmenter section (not shown) among other systems orfeatures. The fan section 322 drives an inlet airflow to split with abypass portion being driven along an outboard bypass flow path, whilethe core portion is further driven by a compressor section 324 along acore flow path for compression and communication into the combustorsection 326. The hot combustion gases generated in the combustor section326 are expanded through the turbine section 328. Although depicted as aturbofan gas turbine engine in the disclosed non-limiting embodiment, itshould be understood that the concepts described herein are not limitedto turbofan engines and these teachings could extend to other types ofengines, including but not limited to, geared turbine engines having ageared architecture 348, three-spool engine architectures, andground-based engines.

The exemplary fan section comprises a fan case 335 surrounding a fan 340which comprises a circumferential array of fan blades 342. In theexemplary two-spool engine, the low pressure spool 330 comprises a shaft331 rotatable about axis A joining a first (or low) pressure compressor(LPC) section 338 to a first (or low) pressure turbine (LPT) section339. Similarly, a second (or high) speed spool 332 comprises a shaft 333rotatable about axis A coupling a second (or high) pressure compressorsection 352 to the high pressure turbine section 354.

The core airflow is compressed by the low pressure compressor 338 thenthe high pressure compressor 352, mixed and burned with fuel in thecombustor 326, then expanded over the high pressure turbine 354 and lowpressure turbine 339. The turbines 354, 339 rotationally drive therespective low speed spool 330 and high speed spool 332 in response tothe expansion. It will be appreciated that each of the positions of thefan section 322, compressor section 324, combustor section 326, turbinesection 328, and fan drive gear system 348 may be varied. For example,gear system 348 may be located aft of combustor section 326 or even aftof turbine section 328, and fan section 322 may be positioned forward oraft of the location of gear system 348.

In a non-limiting embodiment, the FIG. 11 gas turbine engine 320 is ahigh-bypass geared aircraft engine. In a further example, the gasturbine engine 320 bypass ratio is greater than about six (6:1). Thegeared architecture 348 can include an epicyclic gear train, such as aplanetary gear system or other gear system. The example epicyclic geartrain has a gear reduction ratio of greater than about 2.3:1, and inanother example is greater than about 2.5:1. The exemplary gearedarchitecture transmits driving torque from the low pressure spool to thefan with a geared reduction. The geared turbofan enables operation ofthe low speed spool 330 at higher speeds, which can increase theoperational efficiency of the low pressure compressor 338 and lowpressure turbine 339 and render increased pressure in a fewer number ofstages. It should be understood, however, that the above parameters areonly exemplary of one embodiment of a geared architecture engine andthat the present invention is applicable to other gas turbine enginesincluding direct drive turbofans.

In one non-limiting embodiment, the bypass ratio of the gas turbineengine 320 is greater than about ten (10:1), the fan diameter issignificantly larger than that of the low pressure compressor 338, andthe low pressure turbine 339 has a pressure ratio that is greater thanabout five (5:1). Low pressure turbine pressure ratio is pressuremeasured prior to inlet of low pressure turbine 339 as related to thepressure at the outlet of the low pressure turbine 339 prior to anexhaust nozzle. It should be understood, however, that the aboveparameters are only exemplary of one embodiment of a geared architectureengine and that the present disclosure is applicable to other gasturbine engines, including direct drive turbofans.

In this embodiment of the exemplary gas turbine engine 320, asignificant amount of thrust is provided by the bypass flow path B dueto the high bypass ratio. The fan section 322 of the gas turbine engine320 is designed for a particular flight condition—typically cruise atabout 0.8 Mach and about 35,000 feet. This flight condition, with thegas turbine engine 320 at its best fuel consumption, is also known asbucket cruise thrust specific fuel consumption (TSFC). TSFC is anindustry standard parameter of fuel consumption per unit of thrust theengine produces at that minimum point.

Fan pressure ratio (FPR) is the pressure ratio across an airfoil of thefan section 322 without the use of a fan exit guide vane (FEGV) system.The low fan pressure ratio according to one non-limiting embodiment ofthe example gas turbine engine 320 is less than 1.45. Low corrected fantip speed (LCFTS) is the actual fan tip speed divided by an industrystandard temperature correction of [(Tram ° R)/(518.7° R)]^(0.5). Thelow corrected fan tip speed according to one non-limiting embodiment ofthe example gas turbine engine 320 is less than about 1150 fps (350m/s).

Airfoils are used throughout the fan, compressor and turbine sections340, 338, 328 within the bypass and core flow paths. The airfoils can besupported relative to the engine static structure 336 or spools using avariety of techniques. Turning now to FIGS. 1A-1B, an engine airfoilelement 20, for example, a blade or a vane, extends in a radialdirection R, or spanwise, from at least one flow path surface 22, forexample, a platform or a shroud, to, for example, a tip 24 or a shroud.The airfoil element 20 includes an airfoil 21 having leading andtrailing edges 26, 28 spaced apart in in a chord-wise direction H. Inthe case of a blade, the tip 24 is arranged adjacent to a blade outerair seal.

The airfoil 21 includes pressure (typically concave) and suction(typically convex) sides 30, 32 spaced apart in an airfoil thicknessdirection T, generally perpendicular to the chord-wise direction H, thatare joined at the leading and trailing edges 26, 28. Multiple airfoils21 are arranged circumferentially in a circumferential direction C in anarray.

As shown in FIG. 1A, the airfoil 20 has a radial span R_(S) and a chordlength L_(C). An inner or outer platform or a shroud may be provided atone or both radial extremities of the airfoil 20, depending upon theapplication (see, e.g., FIGS. 3-5C). R_(S) may be defined as the minimumradial distance between the radially outboard-most portion of airfoil20, which may be the tip 24 in the case of a blade, to the radiallyinboard-most portion of the airfoil 20. The radially inboard- oroutboard-most portion may be an end supported by elastomeric pottingmaterial and an inner or outer ring, or a vane having an integral inneror outer shroud. Alternatively, both ends of the airfoil may besupported in radially spaced rings by potting. R_(S) may be defined asexcluding any fillet that adjoins the airfoil's aerodynamic exteriorsurface to any inner or outer platform or shroud. L_(C) may be definedas the distance from the leading edge 26 to the trailing edge 28 atabout 50% span. For example, R_(S) is 0.75-0.85 inch (19.1-21.6 mm) andL_(C) is 0.56-0.66 inch (14.2-16.8 mm). In one example, the airfoils 20in the array may be configured to provide an asymmetry to reduceundesired vibrations, for example, by arranging airfoils slightlydifferent geometries in a circumferentially alternating pattern. In oneexample, first and second sets of airfoils are interleaved with one setof airfoils having an L_(C) that is less the L_(C) of the other set ofairfoils by 0.001 inch (0.03 mm) or less.

FIG. 2 schematically illustrates one example fan section 340 andcompressor section 324 in more detail. An array of fan exit stator (FES)341 are provided at an inlet of the core flow path downstream from thefan 342. Variable inlet guide vanes (IGV) 343, adjustable usingactuators 345, are arranged fluidly between the FESs 341 and the LPC338. In the disclosed example, the LPC 338 has three stages ofalternating arrays of rotating blades (338 a, 338 c, 338 e) and fixedstator vanes (338 b, 338 d, 338 f), and the HPC 352 has eight stages ofalternating arrays of rotating blades (352 a, 352 c, 352 e, 352 g, 352i, 352 k, 352 m, 352 o) and fixed stator vanes (352 b, 352 d, 352 f, 352h, 352 j, 3521, 352 n, 352 p). A different number of stages or adifferent configuration of blades and vanes can be used if desired.

The fan blades 342 include roots (not shown) that are received in aslotted hub 337 (FIG. 3). In the example compressor section 324, theblades in the LPC 338 and HPC 352 are integrally bladed rotors (FIG. 4A)in which the airfoils are integrally formed with the rotor as a unitarystructure, rather than rooted blades (FIG. 4B) that are received incorrespondingly shaped slots in a rotor. The stator vanes in thecompressor section 324 are cantilevered (FIG. 5A) such that each airfoilextends radially inward from an outer shroud 360 supported by an outercase 362 to a tip 364 that is supported by a potting material within aninner diameter ring (not shown). The eighth stage HPC stator 352 p maybe a “ringed” stator (e.g., “ring-strut-ring”; FIGS. 5B and 9A-9B) arrayin which an inner shroud 366 also is provided at an inner diameter ofthe airfoils, to be joined to one another. The IGV 343 is pivotallysupported by the inner and outer shrouds 360, 366 for rotation about agenerally radially oriented axis 368 (FIG. 5C).

The airfoil may be formed using any suitable process, for example,casting, forging and/or machining. Any suitable material can be used toprovide the airfoil and may be determined based upon factors such asairfoil stresses, engine operating speeds, gas flow dynamics andoperating temperatures. In one example, airfoils in the fan section areconstructed from an aluminum-based alloy, airfoils in the low pressurecompressor section are constructed from an aluminum-based alloy, andairfoils in the high pressure compressor section are constructed from anickel-based superalloy. One example aluminum-based alloy is 7075 with adensity of about 0.103 lb/in³ (2.85 g/cm³) and a modulus of elasticityof about 10.4 Mpsi (71 GPa) at room temperature. One exampletitanium-based alloy is Ti-6Al-4V, which has a density of about 0.16lb/in³ (4.4 g/cm³) and a modulus of elasticity of about 16-17 Mpsi(110-117 GPa) at room temperature. Example nickel-based superalloys areInconel 718 and ME 16. These nickel-based superalloys have a density ofapproximately 0.3 lb/in³ (8.3 g/cm³), and more broadly 0.28-0.32 lb/in³(7.7-8.9 g/cm³). In addition, the nickel-based superalloy material has amodulus of elasticity of approximately 30 Mpsi (206 GPa), and morebroadly 27-36 Mpsi (186-248 GPa) at room temperature. The airfoils mayalso have a coating system.

A resonant condition is where a frequency of the excitation coincideswith a frequency of the airfoil, and may result in high vibratorystress. The airfoil has a number of frequencies that can be resonant atvarious speeds. There are various modes of vibration, each with itsassociated natural frequency. As for airfoils, generally six vibratorymodes primarily reflect how the airfoils interact with each other, andwith other components of the engine. The type (EB, T, SWB, CWB, ND) andnumber (1, 2, 3, etc.) of the various modes may be orderedinterchangeably through this disclosure (e.g., 1EB is the same as EB1).

A first type of mode is easywise bending (EB). An airfoil can beapproximated as a cantilevered beam extending in the radial directionfor the engine. The easywise bending is parallel to the shortestdimension, or in the thickness direction T.

FIGS. 6A-6E illustrate various easywise bending modes. FIG. 6B showsbi-directional movement in the direction 520 with a neutral conditionthat is, without deflection, shown in solid lines. FIG. 6B also showsone of two extremes, that is, with relatively extreme deflection inbroken lines. FIG. 6A is a plan view of the airfoil, illustrating nodeline 522, which is the location of each node in cross sections of theairfoil having deflections illustrated in FIG. 6C. FIG. 6C shows bothextremes of EB1 (1EB) movement in broken lines. A first EB mode (EB1 or1EB; FIG. 6C) is the EB mode of lowest frequency. A second EB mode (2EBor EB2; FIG. 6D) deflection, is a mode that encompasses two node lines522A and 522B. The mode has one portion of the airfoil moving toward thepressure side and another toward the suction side, changing directionfor each cycle of vibration. Note there is no corresponding plan viewillustrating the node lines 522A and 522B, though the locations of thetwo horizontal node lines relative to the airfoil height is readilyapparent. EB3 or 3EB (FIG. 6E) is a further EB mode and illustratesthree node lines 522A, 522B, and 522C. Other EB modes may exist, and themode number is indicated by the numeral following “EB.”

The twist or torsion (T) modes (FIGS. 7A and 7B) involve bi-directionaltwist in direction 540 twist generally about a spanwise axis for theairfoil, which is a radial axis from the center of the airfoil, or nodeline 542. As with FIG. 6B, one torsional extreme is shown in brokenlines with the neutral, deflection free condition shown in solid linesas shown in FIG. 7B. As with EB and other modes, there are a series oftorsion modes, including 1T (T1), 2T (T2), etc.

The stiffwise bending (SWB) modes (FIGS. 8A and 8B) are generally normalto the EB modes in the chordwise direction H such that the corners ofthe airfoil tip at the leading and trailing edges remain in-plane. TheSWB resonance frequencies will be higher than the corresponding EBresonance frequencies. As with FIG. 6B, FIG. 8B shows bi-directionalmovement in a direction 530 with one extreme (a trailing-edge shiftedextreme) shown in broken lines relative to a solid line neutralposition. The node line is shown as 532. As with EB and other modes,there are a series of stiffwise bending modes, including 1SWB (SWB1),2SWB (SWB2), etc.

There are other modes as well. The chordwise bending (CWB) mode arewhere the corners of the airfoil tip at the leading and trailing edgesvibrate out-of-plane in the same direction at the same time. As with EBand other modes, there are a series of chordwise bending modes,including 1CWB (CWB1), 2CWB (CWB2), etc. Trailing edge bending (TEB)modes are bending modes that bend primarily along the trailing edge, andleading edge bending (LEB) modes are bending modes that bend primarilyalong the leading edge. Some modes may be a more complex combination ofbending and torsion such that the complex mode (M) cannot becharacterized as one mode. In another example, a nodal diameter (ND)bending mode (FIGS. 9A and 9B) has movement in an axial direction. Sinceone of the inner and outer platforms 360, 362 of the stator vanes arefixed to the outer case 362, the joined inner shrouds 366 can vibrate inunison axially forward and aft in a zero nodal diameter (ND0 or 0ND).Another type of nodal diameter is referred to as an aliased nodaldiameter, which corresponds to the upstream blade count minus the statorcount of the stage in question. In one example, for a stage with 117stator vanes with sixty-six upstream blades in the adjacent stage, thealiased nodal diameter is fifty-one (ND51 or 51ND). In this aliasednodal diameter, there is are fifty-one peaks/troughs vibrating in theradial direction at each of the inner and outer diameters of the statorstage. In the case of stator vanes, where the presence of the shroud hasa significant impact on the vibrational mode, the mode in Table 1 alsoincludes the designation —SH. As a general matter, however, the lowestresonance frequency is expected to be that of the EB1 mode. Theremaining details of airfoil configuration may influence the relativepositioning of the remaining modes.

Table I below and FIG. 10 provide parameters of the particular resonanceprofile:

TABLE I Zero Speed Idle Nominal Min Cruise Redline Nominal Freq. NominalFreq. Nominal Freq. Freq. (Hz) @ speed (Hz) @ speed (Hz) @ speed Mode(Hz) range (rpm) range (rpm) range (rpm) 1EB 2740 2684 2593 2512 1TEB-SH5956 5835 5638 5460 1T 6554 6422 6205 6009 1CWB-SH 31959 31311 3025429299

The above frequencies relate primarily to the airfoils. The frequenciesalso include the effects of a root, platform, rim, disk and/or rotor. Inthe case of a stator vane, where the effects of the shroud have anappreciable effect, “—SH” is indicated under “Mode” in the tables. Inthe case of an array with an asymmetrical arrangement of airfoils, theabove frequencies represent an average of the frequencies of thedifferent airfoils. Tolerance for the nominal frequencies around thesenominal values at each of these speeds is ±10%, more narrowly, ±5%.Exemplary zero speed frequencies are at ambient conditions (e.g., 20-28°C.). For the engine using this airfoil element, exemplary running speedsfor the high spool 332 are: idle speed is 13300-14800 rpm; min. cruisespeed is 18200-20200 rpm; and redline speed is 21300-23700 rpm.

While frequencies are a function of the airfoil length, stiffness, andmass, they also represent the unique design characteristic of theairfoil. During the airfoil design, the resonance frequencies may bemodified by selective modification of the airfoil root stiffness,length, chord, external thickness, or internal features (such as but notlimited to rib location/thickness, or wall thickness, etc.). Any changesto the resonance frequencies could render the airfoil unacceptable forcontinued operation in the field without high vibratory stresses whichcan result in high cycle fatigue cracking. One skilled in vibrationanalysis and design would understand that these resonance frequencycharacteristics are unique for each airfoil and should account for, forexample, the specific operational vibratory environment. The frequenciesare determined using computer modelling, for example, ANSYS, althoughthe frequencies may be measured experimentally.

FIG. 10 is a Campbell diagram, with frequency and rotational speed onthe axes, which plots the resonant frequencies for the airfoil againstengine rotor speed. That is, the Campbell diagram illustrates the uniquefrequency characteristics of the airfoil and captures the vibratoryresonance of the airfoil. The modal frequencies change with speedbecause of the increased temperature (reducing frequency) andcentrifugal stiffening (increasing the frequency). The frequencies(which, as indicated, are unique for each airfoil) are represented byessentially horizontal lines 420, 422, 424, 426, 428, and 430. Theseillustrate, against the engine rotor speed, the frequency of the 1steasy-wise bending (1EB), 1st stiff-wise bending (SWB), 1st torsion (1T),2nd easy-wise bending (2EB), 2nd torsion (2T), and 2nd trailing edgebending (2TEB) vibratory modes, or any other modes relevant to theairfoil, for example, summarized in Table I. However, the sequence ofthe modes or type of mode varies and may be different for each airfoil.The Campbell diagram has angled lines 400, 402, 404, 406, 408, 410, 412,414, and 416. These angled lines, called excitation orders, representthe excitation from upstream and downstream stationary airfoils or otherinterruptions in the flowpath that the airfoil feels as it rotates pastthe stationary airfoils.

For example, lines 400, 402, and 404 may be components of a once perrevolution excitation. The airfoils can feel this excitation forexcitation orders 1E, 2E, 3E, 4E, and 5E. Lines 400, 402, and 404,represent 4E, 6E, and 7E, respectively. In any flowpath, there aregeneral aerodynamic disturbances which the airfoils feel at multiples ofthe rotor spin frequency. 1E is one excitation per revolution or therotor spin frequency (in cycles per second). The airfoils feel multiplesof this once per revolution.

As illustrated for the airfoil, the 6E (402), and 7E (404) excitationorders are plotted on the Campbell diagram and are a potential concernbecause there are resonance crossings with the first bending mode (line420) at high speed. The 4E line (line 400) does not have a crossing andis of less significance.

In addition, lines 410 and 412 respectively are excitation functionsthat are proportional to the vane counts of the vane stages immediatelyupstream and downstream of the airfoil stage in question. Lines 414 and416 are twice 410 and 412 excitations and are relevant to Fourierdecomposition of excitations. Lines 406 and 408 are proportional tocounts of downstream struts (which are big structural airfoils that arepart of the bearing supports; in this example, the strut count isdifferent on two halves of the engine circumference).

Where the resonance frequency lines (represented by lines 420, 422, 424,426, 428, and 430) intersect the excitation lines (represented by theangled lines 400, 402, 404, 406, 408, 410, 412, 414, and 416) a resonantcondition occurs, which, as indicated, may result in high vibratorystress. The present airfoil characteristics have been designed such thatvibratory modes, which may result in high vibratory stresses at aresonant condition, are avoided. Accordingly, the modes do not occur inthe normal engine operating speed range (near idle (line 440)) andbetween minimum engine cruise (line 442) and redline (line 444).Vibratory modes, which are not predicted to have a high resonanceresponse, are allowed to have a resonance condition in the normaloperating range. As indicated, these evaluations may account for some ormore of flowpath temperature and pressure, airfoil length, speed, etc.As a result, the evaluation and the subsequent iterative redesign of theairfoil is an airfoil which is unique for a specific engine in aspecific operating condition.

During the design, the airfoil must be tuned such that the resonancepoints do not occur in the operating speed range of the engine forcritical modes. To tune the airfoil, the resonance frequency must bechanged, for example, by varying the airfoil length thickness, moment ofinertia, or other parameters. These parameters are modified until thegraphical intersections representing unwanted resonance occur outsidethe operating speed range, or at least outside key operating conditionswithin the operating speed range. This should be done for each the firstfour (or more) vibratory modes of the airfoil (1EB, 1T, 1CWB, 1SWB), andthe airfoil should be tuned for varying excitation sources.

In FIG. 10, the idle speed is shown as 440, the minimum cruise speed isshown as 442, and the redline speed is shown as 444. Idle speed isimportant because the engine spends much time at idle. Tuning outresonance at min cruise and redline speeds are important because enginestypically cannot avoid these speeds. A resonance at an excitationfrequency at an intermediate speed may be avoided by slightly increasingor decreasing speed.

As an example from FIG. 10, it is seen that there are two resonanceconditions. That is, the 1st stiff-wise bending resonance mode (line422) crosses two excitation lines, which are lines 406 and 408. Thesetwo resonance conditions occur between the engine idle speed (line 440)and the engine minimum cruise speed (line 442). It should be understoodthat regardless of the particular mode, it is desirable to design anairfoil that at least avoids resonance at speed lines 440 and 442.Resonance between lines 440 and 442 is an acceptable location for aresonance to occur and is unique for this airfoil in this engine.

The disclosed airfoil is subject to damage from wear and foreign objectdebris (FOD) during engine operation. Pieces of the airfoil may bebroken off, for example, from the tip, leading edge and/or trailing edgeresulting in an altered or unrestored mode resonance frequency for theairfoil, which deviates from at least one of the desired mode resonancefrequencies indicated in the Table(s). One or more repair procedures areemployed (e.g., welding a piece onto the airfoil and/or machining agrafted piece) to repair the airfoil and restore the geometry andintegrity of the airfoil. The repair procedure restores the unrestoredmode resonance frequency to again correspond to the desired moderesonance frequencies indicated in the Table(s).

It should also be understood that although a particular componentarrangement is disclosed in the illustrated embodiment, otherarrangements will benefit herefrom. Although particular step sequencesare shown, described, and claimed, it should be understood that stepsmay be performed in any order, separated or combined unless otherwiseindicated and will still benefit from the present invention.

Although the different examples have specific components shown in theillustrations, embodiments of this invention are not limited to thoseparticular combinations. It is possible to use some of the components orfeatures from one of the examples in combination with features orcomponents from another one of the examples.

Although an example embodiment has been disclosed, a worker of ordinaryskill in this art would recognize that certain modifications would comewithin the scope of the claims. For that reason, the following claimsshould be studied to determine their true scope and content.

What is claimed is:
 1. A turbomachine airfoil element comprising: anairfoil having pressure and suction sides spaced apart from one anotherin a thickness direction and joined to one another at leading andtrailing edges, the airfoil extending in a radial direction of a spanthat is in a range of 0.75-0.85 inch (19.1-21.6 mm); a chord lengthextending in a chordwise direction from the leading edge to the trailingedge at 50% of the span is in a range of 0.56-0.66 inch (14.2-16.8 mm);and at least two of: a first mode has a frequency of 2740 up to ±10% Hz;a second mode has a frequency of 5956 up to ±10% Hz; a third mode has afrequency of 6554 up to ±10% Hz; and a fourth mode has a frequency of31959 up to ±10% Hz; wherein the frequencies are at a zero speed andambient conditions, and the frequency of any given mode does not exceedthe frequency of a higher order mode; wherein the first mode is a 1EBmode, the second mode is a 1TEB-SH mode, the third mode is a 1T mode,and the fourth mode is a 1CWB-SH mode, the 1EB and 1TEB-SH modescorrespond to deflections substantially parallel to thickness direction,the 1CWB-SH modes correspond to bending that is substantially normal tothe thickness direction and substantially along the chordwise direction,and the 1T mode corresponds to twisting the radial direction; whereinthe airfoil element is part of a cantilevered stator vane; wherein theairfoil is a nickel-based superalloy, the nickel-based superalloy has adensity of 0.28-0.32 lb/in³ (7.7-8.9 g/cm³), the nickel-based superalloyhas a modulus of elasticity of 27-36 Mpsi (186-248 GPa) at roomtemperature.
 2. The element of claim 1, wherein three of the first,second, third and fourth mode frequencies are present.
 3. The element ofclaim 1, wherein at a minimum cruise speed of 18200-20200 rpm at Mach0.8 at 35,000 feet: the first mode has a frequency of 2593 up to ±10%Hz; the second mode has a frequency of 5638 up to ±10% Hz; the thirdmode has a frequency of 6205 up to ±10% Hz; and the fourth mode has afrequency of 30254 up to ±10% Hz.
 4. The element of claim 1, wherein thefrequencies are up to ±5% Hz.
 5. A method of repairing an airfoilcomprising the steps of: providing an airfoil having pressure andsuction sides spaced apart from one another in a thickness direction andjoined to one another at leading and trailing edges, the airfoilextending in a radial direction of a span that is in a range of0.75-0.85 inch (19.1-21.6 mm), and a chord length extending in achordwise direction from the leading edge to the trailing edge at 50% ofthe span is in a range of 0.56-0.66 inch (14.2-16.8 mm), wherein theprovided airfoil has at least one unrestored mode frequency that isattributable to damage to the airfoil; and repairing the airfoil toprovide at least two of: a first mode has a frequency of 2740 up to ±10%Hz; a second mode has a frequency of 5956 up to ±10% Hz; a third modehas a frequency of 6554 up to ±10% Hz; and a fourth mode has a frequencyof 31959 up to ±10% Hz; wherein at least one of the first, second, thirdand fourth mode frequencies corresponds to a restored mode frequencythat supersedes the unrestored mode frequency; wherein the frequenciesare at a zero speed and ambient conditions, and the frequency of anygiven mode does not exceed the frequency of a higher order mode; whereinthe first mode is a 1EB mode, the second mode is a 1TEB-SH mode, thethird mode is a 1T mode, and the fourth mode is a 1CWB-SH mode, the 1EBand 1TEB-SH modes correspond to deflections substantially parallel tothickness direction, the 1CWB-SH modes correspond to bending that issubstantially normal to the thickness direction and substantially alongthe chordwise direction, and the 1T mode corresponds to twisting theradial direction; wherein the airfoil element is part of a cantileveredstator vane; wherein the airfoil is a nickel-based superalloy, thenickel-based superalloy has a density of 0.28-0.32 lb/in³ (7.7-8.9g/cm³), the nickel-based superalloy has a modulus of elasticity of 27-36Mpsi (186-248 GPa) at room temperature.
 6. A turbofan engine comprising:a fan section; a compressor section arranged fluidly downstream from thefan section; a turbine section arranged fluidly downstream from thecompressor section; a combustor arranged fluidly between the compressorand turbine sections; and an airfoil in at least one of the fan,compressor and turbine sections, the airfoil having: pressure andsuction sides spaced apart from one another in a thickness direction andjoined to one another at leading and trailing edges, the airfoilextending in a radial direction of a span that is in a range of0.75-0.85 inch (19.1-21.6 mm); a chord length extending in a chordwisedirection from the leading edge to the trailing edge at 50% of the spanis in a range of 0.56-0.66 inch (14.2-16.8 mm); and at least two of: afirst mode has a frequency of 2740 up to ±10% Hz; a second mode has afrequency of 5956 up to ±10% Hz; a third mode has a frequency of 6554 upto ±10% Hz; and a fourth mode has a frequency of 31959 up to ±10% Hz;wherein the frequencies are at a zero speed and ambient conditions, andthe frequency of any given mode does not exceed the frequency of ahigher order mode; wherein the first mode is a 1EB mode, the second modeis a 1TEB-SH mode, the third mode is a 1T mode, and the fourth mode is a1CWB-SH mode, the 1EB and 1TEB-SH modes correspond to deflectionssubstantially parallel to thickness direction, the 1CWB-SH modescorrespond to bending that is substantially normal to the thicknessdirection and substantially along the chordwise direction, and the 1Tmode corresponds to twisting the radial direction; wherein the airfoilis provided in the compressor section, the compressor section includes ahigh pressure compressor fluidly downstream from a low pressurecompressor, and the airfoil is in the high pressure compressor, the highpressure compressor includes eight stages, the airfoil is part of astator, and the stator is a cantilevered stator vane; wherein theairfoil is a nickel-based superalloy, the nickel-based superalloy has adensity of 0.28-0.32 lb/in³ (7.7-8.9 g/cm³), the nickel-based superalloyhas a modulus of elasticity of 27-36 Mpsi (186-248 GPa) at roomtemperature.